It turns out there needed to be more groundwork than I had anticipated before hitting the Chinese Remainder Theorem. This lesson introduces modular arithmetic, and the Chinese Remainder Theorem will be covered later. I will also be taking a detour to cover all of the math inherent to RSA encryption algorithms in the coming months.
The results for testing numbers for divisibility in base 10 are laid out here. It appears we’ll be reaching the rational numbers at some point in the spring of 2012.
The fifteenth lesson of the Math From Scratch series, dealing with the Fundamental Theorem of Arithmetic, is available here.
As some of you know, I have bilateral elbow tendinitis. As a result, I need to reduce the amount of time spent sitting in front of a keyboard. Unfortunately, this has forced me to slow down on the “Math From Scratch” series. From this point on, new lessons will appear on the first of each month, with lesson 15 due November 1. July and August, the “Summer school” month, will be skipped. Thus, there will now be ten lessons per year. Check the Bureau 42 calendar for updates.
The next chapter in the Math From Scratch series is available here. We can now define a division algorithm involving remainder.
We can finally define distances, which allows us to establish the number line. Those tools are presented in lesson 13: Metric Spaces Other Than Canada.
With the bases representation theorem established, we can examine the bases that are common to computer science, and how they have plagued some of the more adept Nintendo players of by generation. Lesson 12: Other Bases.
This week’s lesson discusses the future of all norm referenced testing, and much criterion referenced testing.